‘Win’ Your Fantasy Football Auction Draft
with Integer Programming and R
Major Dusty Turner
Department of Statistical Science at Baylor University
In this talk we’ll win your fantasy football league using
ESPN API
Integer Programming
and
R
In this talk we’ll win your fantasy football league using
ESPN API
Integer Programming
and
R
But first…
I went for a run today…
So I went for a run today…
A little about me
Professional Life
- Engineer Officer
- Training: Fort Leonard Wood Missouri
- Platoon Leader: Hawaii (Iraq)
- Company Commander: White Sands Missile Range, NM (Afghanistan)
- Assistant Professor / Instructor
- United States Miliary Academy, West Point, NY
- Operations Research Systems Analyst (ORSA)
- Center for Army Analysis: Fort Belvoir, VA
Educational Life
- United States Military Academy, 2007
- BS Operations Research
- University of Missouri of Science and Technology, 2012
- MS Engineering Management
- THE Ohio State, 2016
- MS Integrated Systems Engineering
- Applied Statistics Minor
- Baylor University, 2025 (Hopefully)
- Statistics PhD Student
Best Life
- Married Jill (2010)
- Xichigan
- Epic / Mayo Clinic
- Cal (2013)
- New Mexico
- All Sports
- Reese (2015)
- Ohio
- Dance / Sports
What I assume about you…
Football
Fantasy Football
Integer Programming
RStats
What I assume about you…
Football
What I assume about you…
Football
Fantasy Football
Integer Programming
RStats
What I assume about you…
Fantasy Football
What I assume about you…
Football
Fantasy Football
Integer Programming
RStats
What I assume about you…
Integer Programming
What I assume about you…
Football
Fantasy Football
Integer Programming
RStats
What I assume about you…
RStats
So what is this fantasy football thing…
I’m glad you asked
Fantasy football is a weekly game where team managers head-to-head with one other member in your league.
Teams score points based off of the real life performance of players on their team.
Teams that score more points than their opponent win.
Roster Make Up
- 1 Quarterbacks
- 2 Running back
- 2 Wide Receiver
- 1 Tight End
- 1 Flex (RB, WR, or TE)
- 1 Defense
- 1 Kicker
- Several bench players
Generally score points for yards gained, touchdowns scored, turnovers, field goals…
How do we select players?
Auction Draft
- Owners have $200 to bid on players auction style
- As players are nominated, the managers willing to spend the most money on the players gets him on their team
- The draft continues until all managers fill out their roster
Snake Draft
Players alternate selecting players until rosters are filled out.
We will look at the auction draft format
There are several strategies
- Spend lots of money on who we think are the best players
- Try to get bargains throughout the draft
- Maybe there’s a more intelligent strategy?
Enter: Integer Programming
Lets make some assumptions
- We know how many points a player is going to score throughout the year
- We know how much each player is worth
Goal: Maximize expected points
Subject to
- Expected cost of each player
- Roster configuration
Other pertinent information
- We do not care about the quality of our bench (spend 0 on bench)
- We are indifferent to our defense and kicker.
Lets get mathy
Maximize: \(\sum{p_{qrwt} * x_{qrwt}}\)
where \(p_{qrwt}\) is the expected points scored for player \(p_{qrwt}\)
\(q = 0, 1, 2, ... q\)
\(r = 0, 1, 2, ... r\)
\(w = 0, 1, 2, ... w\)
\(t = 0, 1, 2, ... t\)
\(x_{qrwt} \in (0,1)\)
Not so fast
Constraints
Football Position Constraints:
\(X_{1rwt} + X_{2rwt} + ... + X_{qrwt} = 1\) \(X_{q1wt} + X_{q2wt} + ... + X_{qrwt} \leq 3\) \(X_{qr1t} + X_{qr2t} + ... + X_{qrwt} \leq 3\) \(X_{qrw1} + X_{qrw2} + ... + X_{qrwt} \leq 2\) \(X_{q111} + X_{q211} + ... + X_{qrwt} = 6\)
Only 1 QB
At most 3 RBs
At most 3 WRs
At most 2 TEs
RB + WR + TE = 6
Financial Constraints
\(\sum_{q=0}^Q\sum_{r=0}^R\sum_{w=0}^W\sum_{t=0}^T C_{qrwt} * X_{qrwt} <= 200 \hspace{1cm}\)
So how do we get player data….?
I’m glad you asked
I’m glad you asked
I’m glad you asked
I’m glad you asked
ESPNGet <- httr::RETRY(
verb = "GET",
url = paste0("https://fantasy.espn.com/apis/v3/games/ffl/seasons/2022/
segments/0/leaguedefaults/3?scoringPeriodId=0&view=kona_player_info"),
query = list(view = "kona_player_info"),
httr::accept_json(),
httr::add_headers(
`X-Fantasy-Filter` = jsonlite::toJSON(
x = list(players = list(limit = 500,
sortPercOwned = list(sortAsc = FALSE,
sortPriority = 1
))),
auto_unbox = TRUE))
)I’m glad you asked
ESPNGet <- httr::RETRY(
verb = "GET",
url = paste0("https://fantasy.espn.com/apis/v3/games/ffl/seasons/2022/
segments/0/leaguedefaults/3?scoringPeriodId=0&view=kona_player_info"),
query = list(view = "kona_player_info"),
httr::accept_json(),
httr::add_headers(
`X-Fantasy-Filter` = jsonlite::toJSON(
x = list(players = list(limit = 500,
sortPercOwned = list(sortAsc = FALSE,
sortPriority = 1
))),
auto_unbox = TRUE)))
ESPNRaw <- rawToChar(ESPNGet$content)
ESPNFromJSON <- jsonlite::fromJSON(ESPNRaw)Make Tibble of 1 Player’s Data
get_player_projection <- function(id){
tibble(fpts = ESPNFromJSON$players$player$stat[[id]]$appliedTotal,
season = ESPNFromJSON$players$player$stat[[id]]$seasonId,
score_per_id = ESPNFromJSON$players$player$stat[[id]]$scoringPeriodId) |>
filter(score_per_id == 0) |>
mutate(player = ESPNFromJSON$players$player$fullName[id]) |>
mutate(position = ESPNFromJSON$players$player$defaultPositionId[id]) |>
filter(season == 2022) |>
filter(fpts == max(fpts)) |>
mutate(value = ESPNFromJSON$players$player$draftRanksByRankType$PPR$auctionValue[id])
}Make Tibble of 1 Player’s Data
get_player_projection <- function(id){
tibble(fpts = ESPNFromJSON$players$player$stat[[id]]$appliedTotal,
season = ESPNFromJSON$players$player$stat[[id]]$seasonId,
score_per_id = ESPNFromJSON$players$player$stat[[id]]$scoringPeriodId) |>
filter(score_per_id == 0) |>
mutate(player = ESPNFromJSON$players$player$fullName[id]) |>
mutate(position = ESPNFromJSON$players$player$defaultPositionId[id]) |>
filter(season == 2022) |>
filter(fpts == max(fpts)) |>
mutate(value = ESPNFromJSON$players$player$draftRanksByRankType$PPR$auctionValue[id])
}Make Tibble of 1 Player’s Data
get_player_projection <- function(id){
tibble(fpts = ESPNFromJSON$players$player$stat[[id]]$appliedTotal,
season = ESPNFromJSON$players$player$stat[[id]]$seasonId,
score_per_id = ESPNFromJSON$players$player$stat[[id]]$scoringPeriodId) |>
filter(score_per_id == 0) |>
mutate(player = ESPNFromJSON$players$player$fullName[id]) |>
mutate(position = ESPNFromJSON$players$player$defaultPositionId[id]) |>
filter(season == 2022) |>
filter(fpts == max(fpts)) |>
mutate(value = ESPNFromJSON$players$player$draftRanksByRankType$PPR$auctionValue[id])
}Make Tibble of 1 Player’s Data
get_player_projection <- function(id){
tibble(fpts = ESPNFromJSON$players$player$stat[[id]]$appliedTotal,
season = ESPNFromJSON$players$player$stat[[id]]$seasonId,
score_per_id = ESPNFromJSON$players$player$stat[[id]]$scoringPeriodId) |>
filter(score_per_id == 0) |>
mutate(player = ESPNFromJSON$players$player$fullName[id]) |>
mutate(position = ESPNFromJSON$players$player$defaultPositionId[id]) |>
filter(season == 2022) |>
filter(fpts == max(fpts)) |>
mutate(value = ESPNFromJSON$players$player$draftRanksByRankType$PPR$auctionValue[id])
}Make Tibble of 1 Player’s Data
get_player_projection <- function(id){
tibble(fpts = ESPNFromJSON$players$player$stat[[id]]$appliedTotal,
season = ESPNFromJSON$players$player$stat[[id]]$seasonId,
score_per_id = ESPNFromJSON$players$player$stat[[id]]$scoringPeriodId) |>
filter(score_per_id == 0) |>
mutate(player = ESPNFromJSON$players$player$fullName[id]) |>
mutate(position = ESPNFromJSON$players$player$defaultPositionId[id]) |>
filter(season == 2022) |>
filter(fpts == max(fpts)) |>
mutate(value = ESPNFromJSON$players$player$draftRanksByRankType$PPR$auctionValue[id])
}Make Tibble of 1 Player’s Data
get_player_projection <- function(id){
tibble(fpts = ESPNFromJSON$players$player$stat[[id]]$appliedTotal,
season = ESPNFromJSON$players$player$stat[[id]]$seasonId,
score_per_id = ESPNFromJSON$players$player$stat[[id]]$scoringPeriodId) |>
filter(score_per_id == 0) |>
mutate(player = ESPNFromJSON$players$player$fullName[id]) |>
mutate(position = ESPNFromJSON$players$player$defaultPositionId[id]) |>
filter(season == 2022) |>
filter(fpts == max(fpts)) |>
mutate(value = ESPNFromJSON$players$player$draftRanksByRankType$PPR$auctionValue[id])
}Make Tibble of 1 Player’s Data
get_player_projection <- function(id){
tibble(fpts = ESPNFromJSON$players$player$stat[[id]]$appliedTotal,
season = ESPNFromJSON$players$player$stat[[id]]$seasonId,
score_per_id = ESPNFromJSON$players$player$stat[[id]]$scoringPeriodId) |>
filter(score_per_id == 0) |>
mutate(player = ESPNFromJSON$players$player$fullName[id]) |>
mutate(position = ESPNFromJSON$players$player$defaultPositionId[id]) |>
filter(season == 2022) |>
filter(fpts == max(fpts)) |>
mutate(value = ESPNFromJSON$players$player$draftRanksByRankType$PPR$auctionValue[id])
}Make Tibble of 1 Player’s Data
get_player_projection <- function(id){
tibble(fpts = ESPNFromJSON$players$player$stat[[id]]$appliedTotal,
season = ESPNFromJSON$players$player$stat[[id]]$seasonId,
score_per_id = ESPNFromJSON$players$player$stat[[id]]$scoringPeriodId) |>
filter(score_per_id == 0) |>
mutate(player = ESPNFromJSON$players$player$fullName[id]) |>
mutate(position = ESPNFromJSON$players$player$defaultPositionId[id]) |>
filter(season == 2022) |>
filter(fpts == max(fpts)) |>
mutate(value = ESPNFromJSON$players$player$draftRanksByRankType$PPR$auctionValue[id])
}Show one example for Jared
| fpts | season | score_per_id | jsonid | player | position | value |
|---|---|---|---|---|---|---|
| 258.2525 | 2022 | 0 | 2 | Stefon Diggs | 3 | 44 |
Clean Results for Linear Model
Clean Results for Linear Model
ESPN_results <-
1:length(ESPNFromJSON$players$draftAuctionValue) |>
map_dfr(~get_player_projection(id = .x)) |>
group_by(player) |> slice(1) |> ungroup() |>
mutate(position = case_when(position == 1 ~ "QB",
position == 2 ~ "RB",
position == 3 ~ "WR",
position == 4 ~ "TE",
position == 5 ~ "K",
position == 16 ~ "DEF")) |>
mutate(points_per_dollar = fpts / value) |>
filter(!is.infinite(points_per_dollar)) |>
filter(!is.nan(points_per_dollar)) |>
mutate(position_qb = ifelse(position == "QB",1,0)) |>
mutate(position_rb = ifelse(position == "RB",1,0)) |>
mutate(position_wr = ifelse(position == "WR",1,0)) |>
mutate(position_te = ifelse(position == "TE",1,0)) |>
mutate(position_flex = ifelse(position %in% c("RB","WR","TE"),1,0)) |>
filter(position %in% c("QB","WR","RB","TE")) Example of Results
| fpts | player | value | points_per_dollar | position_qb | position_rb | position_wr | position_te | position_flex |
|---|---|---|---|---|---|---|---|---|
| QB | ||||||||
| 271 | Tua Tagovailoa | 1 | 271 | 1 | 0 | 0 | 0 | 0 |
| 269 | Kirk Cousins | 1 | 269 | 1 | 0 | 0 | 0 | 0 |
| 261 | Derek Carr | 1 | 261 | 1 | 0 | 0 | 0 | 0 |
| 261 | Trevor Lawrence | 1 | 261 | 1 | 0 | 0 | 0 | 0 |
| 253 | Justin Fields | 1 | 253 | 1 | 0 | 0 | 0 | 0 |
| 284 | Trey Lance | 2 | 142 | 1 | 0 | 0 | 0 | 0 |
| 310 | Aaron Rodgers | 3 | 103 | 1 | 0 | 0 | 0 | 0 |
| 307 | Dak Prescott | 3 | 102 | 1 | 0 | 0 | 0 | 0 |
| 307 | Tom Brady | 3 | 102 | 1 | 0 | 0 | 0 | 0 |
| 302 | Russell Wilson | 3 | 101 | 1 | 0 | 0 | 0 | 0 |
| 294 | Joe Burrow | 3 | 98 | 1 | 0 | 0 | 0 | 0 |
| 286 | Matthew Stafford | 3 | 95 | 1 | 0 | 0 | 0 | 0 |
| 319 | Jalen Hurts | 5 | 64 | 1 | 0 | 0 | 0 | 0 |
| 316 | Lamar Jackson | 8 | 40 | 1 | 0 | 0 | 0 | 0 |
| 314 | Kyler Murray | 8 | 39 | 1 | 0 | 0 | 0 | 0 |
| 328 | Justin Herbert | 10 | 33 | 1 | 0 | 0 | 0 | 0 |
| 352 | Patrick Mahomes | 11 | 32 | 1 | 0 | 0 | 0 | 0 |
| 375 | Josh Allen | 18 | 21 | 1 | 0 | 0 | 0 | 0 |
| WR | ||||||||
| 164 | Treylon Burks | 1 | 164 | 0 | 0 | 1 | 0 | 1 |
| 163 | Marvin Jones Jr. | 1 | 163 | 0 | 0 | 1 | 0 | 1 |
| 159 | Jahan Dotson | 1 | 159 | 0 | 0 | 1 | 0 | 1 |
| 157 | Robbie Anderson | 1 | 157 | 0 | 0 | 1 | 0 | 1 |
| 151 | Joshua Palmer | 1 | 151 | 0 | 0 | 1 | 0 | 1 |
| 146 | DeVante Parker | 1 | 146 | 0 | 0 | 1 | 0 | 1 |
| 145 | Jarvis Landry | 1 | 145 | 0 | 0 | 1 | 0 | 1 |
| 185 | Brandon Aiyuk | 2 | 92 | 0 | 0 | 1 | 0 | 1 |
| 180 | Chase Claypool | 2 | 90 | 0 | 0 | 1 | 0 | 1 |
| 180 | Robert Woods | 2 | 90 | 0 | 0 | 1 | 0 | 1 |
| 175 | Garrett Wilson | 2 | 88 | 0 | 0 | 1 | 0 | 1 |
| 174 | Chris Olave | 2 | 87 | 0 | 0 | 1 | 0 | 1 |
| 174 | Jakobi Meyers | 2 | 87 | 0 | 0 | 1 | 0 | 1 |
| 173 | Allen Lazard | 2 | 86 | 0 | 0 | 1 | 0 | 1 |
| 172 | Marquez Valdes-Scantling | 2 | 86 | 0 | 0 | 1 | 0 | 1 |
| 169 | Russell Gage | 2 | 84 | 0 | 0 | 1 | 0 | 1 |
| 168 | Tyler Boyd | 2 | 84 | 0 | 0 | 1 | 0 | 1 |
| 157 | Michael Gallup | 2 | 78 | 0 | 0 | 1 | 0 | 1 |
| 150 | DeAndre Hopkins | 2 | 75 | 0 | 0 | 1 | 0 | 1 |
| 146 | DJ Chark | 2 | 73 | 0 | 0 | 1 | 0 | 1 |
| 135 | Skyy Moore | 2 | 67 | 0 | 0 | 1 | 0 | 1 |
| 186 | Kadarius Toney | 3 | 62 | 0 | 0 | 1 | 0 | 1 |
| 197 | Tyler Lockett | 5 | 39 | 0 | 0 | 1 | 0 | 1 |
| 192 | DeVonta Smith | 5 | 38 | 0 | 0 | 1 | 0 | 1 |
| 198 | Elijah Moore | 6 | 33 | 0 | 0 | 1 | 0 | 1 |
| 199 | Hunter Renfrow | 6 | 33 | 0 | 0 | 1 | 0 | 1 |
| 197 | JuJu Smith-Schuster | 6 | 33 | 0 | 0 | 1 | 0 | 1 |
| 198 | Rashod Bateman | 6 | 33 | 0 | 0 | 1 | 0 | 1 |
| 192 | Adam Thielen | 6 | 32 | 0 | 0 | 1 | 0 | 1 |
| 193 | Drake London | 6 | 32 | 0 | 0 | 1 | 0 | 1 |
| 207 | Michael Thomas | 7 | 30 | 0 | 0 | 1 | 0 | 1 |
| 201 | Allen Robinson II | 7 | 29 | 0 | 0 | 1 | 0 | 1 |
| 200 | Christian Kirk | 7 | 29 | 0 | 0 | 1 | 0 | 1 |
| 199 | Amari Cooper | 7 | 28 | 0 | 0 | 1 | 0 | 1 |
| 207 | Gabe Davis | 11 | 19 | 0 | 0 | 1 | 0 | 1 |
| 212 | Darnell Mooney | 12 | 18 | 0 | 0 | 1 | 0 | 1 |
| 209 | Amon-Ra St. Brown | 13 | 16 | 0 | 0 | 1 | 0 | 1 |
| 198 | Chris Godwin | 13 | 15 | 0 | 0 | 1 | 0 | 1 |
| 210 | Courtland Sutton | 15 | 14 | 0 | 0 | 1 | 0 | 1 |
| 212 | Jerry Jeudy | 15 | 14 | 0 | 0 | 1 | 0 | 1 |
| 212 | DK Metcalf | 17 | 12 | 0 | 0 | 1 | 0 | 1 |
| 212 | Marquise Brown | 17 | 12 | 0 | 0 | 1 | 0 | 1 |
| 215 | Brandin Cooks | 22 | 10 | 0 | 0 | 1 | 0 | 1 |
| 218 | Jaylen Waddle | 22 | 10 | 0 | 0 | 1 | 0 | 1 |
| 211 | Mike Williams | 22 | 10 | 0 | 0 | 1 | 0 | 1 |
| 218 | Diontae Johnson | 23 | 9 | 0 | 0 | 1 | 0 | 1 |
| 236 | Michael Pittman Jr. | 26 | 9 | 0 | 0 | 1 | 0 | 1 |
| 222 | Terry McLaurin | 25 | 9 | 0 | 0 | 1 | 0 | 1 |
| 221 | A.J. Brown | 26 | 8 | 0 | 0 | 1 | 0 | 1 |
| 235 | DJ Moore | 30 | 8 | 0 | 0 | 1 | 0 | 1 |
| 237 | Tee Higgins | 31 | 8 | 0 | 0 | 1 | 0 | 1 |
| 238 | Keenan Allen | 32 | 7 | 0 | 0 | 1 | 0 | 1 |
| 223 | Mike Evans | 30 | 7 | 0 | 0 | 1 | 0 | 1 |
| 252 | CeeDee Lamb | 40 | 6 | 0 | 0 | 1 | 0 | 1 |
| 254 | Davante Adams | 45 | 6 | 0 | 0 | 1 | 0 | 1 |
| 261 | Deebo Samuel | 44 | 6 | 0 | 0 | 1 | 0 | 1 |
| 258 | Stefon Diggs | 44 | 6 | 0 | 0 | 1 | 0 | 1 |
| 246 | Tyreek Hill | 38 | 6 | 0 | 0 | 1 | 0 | 1 |
| 313 | Cooper Kupp | 59 | 5 | 0 | 0 | 1 | 0 | 1 |
| 276 | Ja'Marr Chase | 54 | 5 | 0 | 0 | 1 | 0 | 1 |
| 288 | Justin Jefferson | 55 | 5 | 0 | 0 | 1 | 0 | 1 |
| 41 | Rashid Shaheed | NA | NA | 0 | 0 | 1 | 0 | 1 |
| K | ||||||||
| 148 | Evan McPherson | 1 | 148 | 0 | 0 | 0 | 0 | 0 |
| 148 | Matt Gay | 1 | 148 | 0 | 0 | 0 | 0 | 0 |
| 145 | Harrison Butker | 1 | 145 | 0 | 0 | 0 | 0 | 0 |
| 144 | Justin Tucker | 1 | 144 | 0 | 0 | 0 | 0 | 0 |
| 141 | Nick Folk | 1 | 141 | 0 | 0 | 0 | 0 | 0 |
| 139 | Brandon McManus | 1 | 139 | 0 | 0 | 0 | 0 | 0 |
| 139 | Daniel Carlson | 1 | 139 | 0 | 0 | 0 | 0 | 0 |
| 134 | Matt Prater | 1 | 134 | 0 | 0 | 0 | 0 | 0 |
| 132 | Graham Gano | 1 | 132 | 0 | 0 | 0 | 0 | 0 |
| 132 | Tyler Bass | 1 | 132 | 0 | 0 | 0 | 0 | 0 |
| 45 | Cameron Dicker | NA | NA | 0 | 0 | 0 | 0 | 0 |
| 15 | Taylor Bertolet | NA | NA | 0 | 0 | 0 | 0 | 0 |
| TE | ||||||||
| 147 | Dawson Knox | 1 | 147 | 0 | 0 | 0 | 1 | 1 |
| 146 | Hunter Henry | 1 | 146 | 0 | 0 | 0 | 1 | 1 |
| 146 | Irv Smith Jr. | 1 | 146 | 0 | 0 | 0 | 1 | 1 |
| 140 | Noah Fant | 1 | 140 | 0 | 0 | 0 | 1 | 1 |
| 136 | Mike Gesicki | 1 | 136 | 0 | 0 | 0 | 1 | 1 |
| 131 | David Njoku | 1 | 131 | 0 | 0 | 0 | 1 | 1 |
| 130 | Tyler Higbee | 1 | 130 | 0 | 0 | 0 | 1 | 1 |
| 146 | Cole Kmet | 2 | 73 | 0 | 0 | 0 | 1 | 1 |
| 144 | Pat Freiermuth | 2 | 72 | 0 | 0 | 0 | 1 | 1 |
| 150 | Dallas Goedert | 3 | 50 | 0 | 0 | 0 | 1 | 1 |
| 148 | Zach Ertz | 3 | 49 | 0 | 0 | 0 | 1 | 1 |
| 168 | T.J. Hockenson | 4 | 42 | 0 | 0 | 0 | 1 | 1 |
| 177 | Dalton Schultz | 5 | 35 | 0 | 0 | 0 | 1 | 1 |
| 188 | Darren Waller | 9 | 21 | 0 | 0 | 0 | 1 | 1 |
| 170 | George Kittle | 8 | 21 | 0 | 0 | 0 | 1 | 1 |
| 198 | Kyle Pitts | 21 | 9 | 0 | 0 | 0 | 1 | 1 |
| 235 | Mark Andrews | 36 | 7 | 0 | 0 | 0 | 1 | 1 |
| 239 | Travis Kelce | 34 | 7 | 0 | 0 | 0 | 1 | 1 |
| DEF | ||||||||
| 144 | Bills D/ST | 1 | 144 | 0 | 0 | 0 | 0 | 0 |
| 136 | Packers D/ST | 1 | 136 | 0 | 0 | 0 | 0 | 0 |
| 128 | Saints D/ST | 1 | 128 | 0 | 0 | 0 | 0 | 0 |
| 125 | Buccaneers D/ST | 1 | 125 | 0 | 0 | 0 | 0 | 0 |
| 120 | Ravens D/ST | 1 | 120 | 0 | 0 | 0 | 0 | 0 |
| 112 | 49ers D/ST | 1 | 112 | 0 | 0 | 0 | 0 | 0 |
| 112 | Cowboys D/ST | 1 | 112 | 0 | 0 | 0 | 0 | 0 |
| 109 | Colts D/ST | 1 | 109 | 0 | 0 | 0 | 0 | 0 |
| 109 | Steelers D/ST | 1 | 109 | 0 | 0 | 0 | 0 | 0 |
| 105 | Dolphins D/ST | 1 | 105 | 0 | 0 | 0 | 0 | 0 |
| RB | ||||||||
| 130 | Raheem Mostert | 1 | 130 | 0 | 1 | 0 | 0 | 1 |
| 169 | AJ Dillon | 2 | 84 | 0 | 1 | 0 | 0 | 1 |
| 163 | Rashaad Penny | 2 | 81 | 0 | 1 | 0 | 0 | 1 |
| 151 | James Robinson | 2 | 76 | 0 | 1 | 0 | 0 | 1 |
| 151 | Michael Carter | 2 | 75 | 0 | 1 | 0 | 0 | 1 |
| 146 | Kenneth Walker III | 2 | 73 | 0 | 1 | 0 | 0 | 1 |
| 145 | Melvin Gordon III | 2 | 72 | 0 | 1 | 0 | 0 | 1 |
| 145 | Nyheim Hines | 2 | 72 | 0 | 1 | 0 | 0 | 1 |
| 127 | James Cook | 2 | 63 | 0 | 1 | 0 | 0 | 1 |
| 184 | Dameon Pierce | 4 | 46 | 0 | 1 | 0 | 0 | 1 |
| 183 | Kareem Hunt | 4 | 46 | 0 | 1 | 0 | 0 | 1 |
| 184 | Rhamondre Stevenson | 4 | 46 | 0 | 1 | 0 | 0 | 1 |
| 181 | Antonio Gibson | 4 | 45 | 0 | 1 | 0 | 0 | 1 |
| 174 | Chase Edmonds | 4 | 44 | 0 | 1 | 0 | 0 | 1 |
| 175 | Damien Harris | 4 | 44 | 0 | 1 | 0 | 0 | 1 |
| 177 | Tony Pollard | 4 | 44 | 0 | 1 | 0 | 0 | 1 |
| 168 | Cordarrelle Patterson | 4 | 42 | 0 | 1 | 0 | 0 | 1 |
| 242 | Josh Jacobs | 10 | 24 | 0 | 1 | 0 | 0 | 1 |
| 189 | Devin Singletary | 9 | 21 | 0 | 1 | 0 | 0 | 1 |
| 185 | Miles Sanders | 9 | 21 | 0 | 1 | 0 | 0 | 1 |
| 197 | Elijah Mitchell | 10 | 20 | 0 | 1 | 0 | 0 | 1 |
| 191 | Clyde Edwards-Helaire | 10 | 19 | 0 | 1 | 0 | 0 | 1 |
| 214 | J.K. Dobbins | 14 | 15 | 0 | 1 | 0 | 0 | 1 |
| 211 | Breece Hall | 19 | 11 | 0 | 1 | 0 | 0 | 1 |
| 214 | Ezekiel Elliott | 20 | 11 | 0 | 1 | 0 | 0 | 1 |
| 205 | Travis Etienne Jr. | 19 | 11 | 0 | 1 | 0 | 0 | 1 |
| 220 | David Montgomery | 21 | 10 | 0 | 1 | 0 | 0 | 1 |
| 216 | Nick Chubb | 24 | 9 | 0 | 1 | 0 | 0 | 1 |
| 243 | Aaron Jones | 32 | 8 | 0 | 1 | 0 | 0 | 1 |
| 228 | Saquon Barkley | 29 | 8 | 0 | 1 | 0 | 0 | 1 |
| 240 | James Conner | 33 | 7 | 0 | 1 | 0 | 0 | 1 |
| 239 | Javonte Williams | 35 | 7 | 0 | 1 | 0 | 0 | 1 |
| 259 | Leonard Fournette | 37 | 7 | 0 | 1 | 0 | 0 | 1 |
| 255 | Alvin Kamara | 46 | 6 | 0 | 1 | 0 | 0 | 1 |
| 254 | D'Andre Swift | 42 | 6 | 0 | 1 | 0 | 0 | 1 |
| 259 | Joe Mixon | 43 | 6 | 0 | 1 | 0 | 0 | 1 |
| 285 | Austin Ekeler | 58 | 5 | 0 | 1 | 0 | 0 | 1 |
| 147 | Cam Akers | 28 | 5 | 0 | 1 | 0 | 0 | 1 |
| 310 | Christian McCaffrey | 59 | 5 | 0 | 1 | 0 | 0 | 1 |
| 258 | Dalvin Cook | 49 | 5 | 0 | 1 | 0 | 0 | 1 |
| 264 | Derrick Henry | 52 | 5 | 0 | 1 | 0 | 0 | 1 |
| 317 | Jonathan Taylor | 61 | 5 | 0 | 1 | 0 | 0 | 1 |
| 265 | Najee Harris | 50 | 5 | 0 | 1 | 0 | 0 | 1 |
| 43 | Caleb Huntley | NA | NA | 0 | 1 | 0 | 0 | 1 |
| 15 | Malik Davis | NA | NA | 0 | 1 | 0 | 0 | 1 |
| 22 | Raheem Blackshear | NA | NA | 0 | 1 | 0 | 0 | 1 |
| 10 | Ronnie Rivers | NA | NA | 0 | 1 | 0 | 0 | 1 |
# A tibble: 1 × 1
`sum(value)`
<int>
1 200[1] 200[1] 111.7315Down to business
Select a solver engine
lpSolve
CVXR
GLPK
rmpk
ompr
lpSolve
library(lpSolve)
f_obj <- ESPN_results |> pull(fpts)
f_con <- matrix(c(ESPN_results |> pull(position_qb),
ESPN_results |> pull(position_qb),
ESPN_results |> pull(position_wr),
ESPN_results |> pull(position_te),
ESPN_results |> pull(position_flex),
ESPN_results |> pull(value)
),nrow = 6, byrow = T)
f_dir <- c("=", # qb
"<=", # rb
"<=", # wr
"=", # te
"=", # flex
"<=" # price
)
f_rhs <- c(1,
3,
3,
1,
6,
200)lpSolve
[1] 220.8450 242.5602 309.6636 192.1663 168.7530 172.5595 201.0691 254.8248
[9] 198.9663 208.8567 181.2622 284.7332 215.0983 184.9182 210.6620 43.0000
[17] 146.7111 252.4529 180.3594 174.0654 198.2010 174.4467 200.0144 309.9427
[25] 190.5999 145.7789 312.9066 167.8848 210.4194 253.6564 306.5225 150.3319
[33] 176.6624 258.4904 183.6543 174.5547 212.1800 187.7119 253.5925 219.9178
[41] 131.4289 146.5585 150.4110 261.4620 260.6069 264.4697 146.4369 188.7177
[49] 192.2315 218.1936 146.0351 234.5686 212.4284 192.7721 197.4233 198.3393
[57] 214.2013 207.2314 175.3097 169.5924 146.3820 199.0347 145.8136 214.3026
[65] 276.1680 159.0293 173.9179 318.5135 240.0416 126.7101 151.1312 144.9516
[73] 238.9946 218.2261 212.2043 294.4468 258.9057 316.9915 374.6255 242.4000
[81] 150.9300 197.0992 253.0926 328.0368 287.7986 186.1823 182.5312 237.6153
[89] 145.9000 269.1750 197.6367 313.9962 316.4061 258.7434 15.4000 235.0536
[97] 172.0591 211.7768 163.0784 285.7049 144.7162 150.5256 156.7192 236.1641
[105] 206.5802 223.3164 135.9019 211.4404 184.6540 265.4768 216.0374 139.8340
[113] 144.6376 144.1705 352.0207 21.6000 130.4284 162.9332 41.4000 197.9605
[121] 183.9000 157.0269 180.4381 10.0000 168.6893 302.4224 227.7660 134.9712
[129] 258.2525 168.0302 237.3114 221.9403 306.8348 177.2297 205.0117 238.7000
[137] 260.7133 284.0327 163.8437 271.0333 168.3101 130.3365 197.0118 246.4522
[145] 148.1828 [,1] [,2] [,3] [,4] [,5] [,6] [,7] [,8] [,9] [,10] [,11] [,12] [,13] [,14]
[1,] 0 0 1 0 0 0 0 0 0 0 0 0 0 0
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[3,] 1 0 0 1 0 1 1 0 1 1 0 0 1 1
[4,] 0 0 0 0 0 0 0 0 0 0 0 0 0 0
[5,] 1 1 0 1 1 1 1 1 1 1 1 1 1 1
[6,] 26 32 3 6 2 2 7 46 7 13 4 58 22 2
[,15] [,16] [,17] [,18] [,19] [,20] [,21] [,22] [,23] [,24] [,25] [,26]
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[5,] 1 1 1 1 1 1 1 1 1 1 1 1
[6,] 19 NA 28 40 2 4 13 2 7 59 10 2
[,27] [,28] [,29] [,30] [,31] [,32] [,33] [,34] [,35] [,36] [,37] [,38]
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[6,] 59 4 15 42 3 3 5 49 4 4 12 9
[,39] [,40] [,41] [,42] [,43] [,44] [,45] [,46] [,47] [,48] [,49] [,50]
[1,] 0 0 0 0 0 0 1 0 0 0 0 0
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[3,] 1 0 0 0 1 1 0 0 1 0 1 1
[4,] 0 0 1 1 0 0 0 0 0 0 0 0
[5,] 1 1 1 1 1 1 0 1 1 1 1 1
[6,] 45 21 1 1 2 44 1 52 1 9 5 23
[,51] [,52] [,53] [,54] [,55] [,56] [,57] [,58] [,59] [,60] [,61] [,62]
[1,] 0 0 0 0 0 0 0 0 0 0 0 0
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[3,] 1 1 1 1 0 1 0 1 1 0 0 1
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[5,] 1 1 1 1 1 1 1 1 1 1 1 1
[6,] 2 30 17 6 10 6 20 11 2 8 1 6
[,63] [,64] [,65] [,66] [,67] [,68] [,69] [,70] [,71] [,72] [,73] [,74]
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[6,] 1 14 54 1 2 5 33 2 2 1 35 22
[,75] [,76] [,77] [,78] [,79] [,80] [,81] [,82] [,83] [,84] [,85] [,86]
[1,] 0 1 0 0 1 0 0 0 1 1 0 0
[2,] 0 1 0 0 1 0 0 0 1 1 0 0
[3,] 1 0 0 0 0 0 1 1 0 0 1 1
[4,] 0 0 0 0 0 0 0 0 0 0 0 0
[5,] 1 0 1 1 0 1 1 1 0 0 1 1
[6,] 15 3 43 61 18 10 1 6 1 10 55 3
[,87] [,88] [,89] [,90] [,91] [,92] [,93] [,94] [,95] [,96] [,97] [,98]
[1,] 0 0 0 1 0 1 1 0 0 0 0 0
[2,] 0 0 0 1 0 1 1 0 0 0 0 0
[3,] 0 1 0 0 0 0 0 0 0 0 1 1
[4,] 0 0 0 0 1 0 0 0 0 1 0 0
[5,] 1 1 1 0 1 0 0 1 1 1 1 1
[6,] 4 32 2 1 21 8 8 37 NA 36 2 17
[,99] [,100] [,101] [,102] [,103] [,104] [,105] [,106] [,107] [,108]
[1,] 0 1 0 0 0 0 0 0 0 0
[2,] 0 1 0 0 0 0 0 0 0 0
[3,] 1 0 0 0 1 1 1 1 0 1
[4,] 0 0 0 0 0 0 0 0 1 0
[5,] 1 0 1 1 1 1 1 1 1 1
[6,] 1 3 2 2 2 26 7 30 1 22
[,109] [,110] [,111] [,112] [,113] [,114] [,115] [,116] [,117] [,118]
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[3,] 0 0 0 0 0 0 0 0 0 0
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[6,] 9 50 24 1 2 2 11 NA 1 2
[,119] [,120] [,121] [,122] [,123] [,124] [,125] [,126] [,127] [,128]
[1,] 0 0 0 0 0 0 0 1 0 0
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[6,] NA 6 4 1 2 NA 2 3 29 2
[,129] [,130] [,131] [,132] [,133] [,134] [,135] [,136] [,137] [,138]
[1,] 0 0 0 0 1 0 0 0 1 1
[2,] 0 0 0 0 1 0 0 0 1 1
[3,] 1 0 1 1 0 0 0 0 0 0
[4,] 0 1 0 0 0 0 0 1 0 0
[5,] 1 1 1 1 0 1 1 1 0 0
[6,] 44 4 31 25 3 4 19 34 1 2
[,139] [,140] [,141] [,142] [,143] [,144] [,145]
[1,] 0 1 0 0 0 0 0
[2,] 0 1 0 0 0 0 0
[3,] 1 0 1 0 1 1 0
[4,] 0 0 0 1 0 0 1
[5,] 1 0 1 1 1 1 1
[6,] 1 1 2 1 5 38 3Solution
Solution
solution <-
lp(
direction = "max",
objective.in = f_obj,
const.mat = f_con,
const.dir = f_dir,
const.rhs = f_rhs,
all.bin = TRUE
)
solution$solution [1] 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0
[38] 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
[75] 0 0 0 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0
[112] 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0My Team
ESPN_results |>
mutate(solution = solution$solution) |>
filter(solution == 1) |>
select(fpts, player, position, value, points_per_dollar) |>
mutate(dollars_per_point = fpts/value) |>
arrange(position)| fpts | player | position | exp_auction_value |
|---|---|---|---|
| 375 | Josh Allen | QB | 18 |
| 317 | Jonathan Taylor | RB | 61 |
| 242 | Josh Jacobs | RB | 10 |
| 239 | Travis Kelce | TE | 34 |
| 313 | Cooper Kupp | WR | 59 |
| 207 | Gabe Davis | WR | 11 |
| 207 | Michael Thomas | WR | 7 |
What’s Next
Round team out with 0 dollar players, k, and def
Handeling uncertainties at the
talk other applicaitons (Afghanistan, Price is Right)
show shiny application put my websight and twitter somewhere get this posted on my websight
